Non-fragile distributed state estimation over sensor networks subject to DoS attacks: the almost sure stability

This paper focuses on the non-fragile distributed state estimation of discrete-time nonlinear systems over sensor networks subject to DoS attacks, whose probabilistic characterisations are adopted to reflect the reality better. On the basis of considering DoS attacks and gain variations, a non-fragile distributed state estimator is designed by fusing the innovation from the adjacent estimators and itself. In light of a switching idea, an auxiliary function on the product term of attack signals is exploited to disclose the evolution of the Lyapunov function. By virtue of the limit theorem and the developed evolution rule, a sufficient condition is proposed to guarantee that the error dynamics are almost surely asymptotical stable. Furthermore, gain variations are handled by utilising the well-known S-procedure, and the desired estimator gains are designed via a set of solutions of matrix inequalities. Finally, the effectiveness of the developed results is illustrated by a numerical example.